Next, we compare our method against three bechmarks: Principal Component Analysis (PCA) [1]}, Canonical Capsules (CaCa) [2]}, and ConDor [3]}.
All prior methods canonicalize clean point clouds with all points on the surface.
To have a fair comparison, we train the above methods on point clouds (P) sampled from NeRF scenes for point on and within the object.
Most scenes have points in the range 90–1200 when sampled uniformly on the \(32^3\)  grid.
We resample the scene when points are less than 1024 and train both Canonical Capsules and ConDor on the resulting point clouds.
CaFi-Net canonicalizes directly over density fields, but we sample a point cloud after canonicalization to compute our metrics.
We follow the same protocol as [3]} to measure and benchmark canonicalization performance for all the methods.
